Abstract
This paper is concerned with the path-dependent shrinking target problems in beta-dynamical systems. For β > 1 let T β be the β-transformation on . Let , and be two positive continuous functions. For any , we show that the set has large intersection property under the condition , where denotes the ergodic sum . Consequently, we can determine the Hausdorff dimension of , which is the solution to some modified pressure function defined through singular value function.
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